Simplify the expression. $(2r^{4}-r^{2}-3r)(-3r^{4}+7r^{3})$
Explanation: First use the distributive property. $ 2 r^4 (-3 r^4) + 2 r^4 (7 r^3) - r^2 (-3 r^4) - r^2 (7 r^3) - 3 r (-3 r^4) - 3 r (7 r^3) $ Simplify. $ - 6r^{8} + 14r^{7} + 3r^{6} - 7r^{5} + 9r^{5} - 21r^{4} $ $-6r^{8}+14r^{7}+3r^{6}+2r^{5}-21r^{4}$ Identify like terms. $ {- 6r^{8}} {+ 14r^{7}} {+ 3r^{6}} {- 7r^{5}} {+ 9r^{5}} {- 21r^{4}} $ Add the coefficients. $ { -6r^{8}} {+ 14r^{7}} {+ 3r^{6}} {+ 2r^{5}} { -21r^{4}} $